Actually after talking with the guy who made that quote I've found he has no idea what he's talking about. — Darkneos

:smile:

Thank you. — Metaphysician Undercover

Think nothing of it (much as you do with math).

In the past I have implored you to write up your math musings and send them off to prestigious journals. The math world languishes without benefit of your folk wisdom. Have you ever followed up on that suggestion? Your fame and fortune await.

Such as reflecting the positive number line over the origin and reversing the sign of the reflected numbers. In other words, positive and negative numbers are opposite numbers. — Andrew M

As I explained, this is an incorrect description because zero is a part of the number line. If zero was not a part of the line, we could say there is two distinct lines, as you seem to be implying, negative and positive lines, one the reflection of the other. But that is not the case. What we have is one line, of which zero is a part. The existence of zero, as a number, means that numbers do not have an opposite number. If numbers have an opposite, what is the opposite of zero?

If numbers have an opposite, what is the opposite of zero? — Metaphysician Undercover

As I quoted from here earlier, zero is its own opposite. Which is to say, -0 + 0 = 0. You can even type it into a calculator and see for yourself.

zero is its own opposite — Andrew M

Sorry Andrew, but "opposites" don't work that way. A thing is the same as itself, it cannot be opposite to itself. "Opposite" requires two.

Sorry Andrew, but "opposites" don't work that way. A thing is the same as itself, it cannot be opposite to itself. "Opposite" requires two. — Metaphysician Undercover

So, according to you, your preferred definition of opposite precludes the mathematical definition of opposite. Even though the subject we are discussing is mathematics.

I really don't think you've provided any "mathematical definition of opposite". But if the mathematical definition of "opposite" allows that a thing is the opposite of itself (as zero is the opposite of zero), then yes, I would say that my preferred definition of "opposite" (the common use of the term) precludes the mathematical definition.

Even though the subject we are discussing is mathematics. — Andrew M

I suppose you ought to produce this mathematical definition of "opposite" so that we can judge whether zero is truly opposite to itself, by that definition. Or whether it is really the case that your preferred definition of "inverse" renders the common definition of "opposite" as inconsistent.

Here's a brief demonstration to help you understand what I am saying. Assume the smallest possible positive number is directly opposed, or inverse, to the largest possible negative number. In other words, we get as close to zero as possible on both sides, and maintain a balance of opposition between the two sides.

Now, let's assume that the quantity represented on each side is so near to nothing (zero) that we might be inclined to round it off. If we do such a thing, then the two quantities on each side become equal to each other, and the same as each other, as zero, instead of opposed to or inverse of one another.

Clearly, two inversely opposed and balancing quantities is not the same thing as one quantity, because that would mean that the positive number closest to zero is exactly the same as the negative number closest to zero, rather than having the two opposed to each other.

I think it's more like you don't know what you're talking about.

Actually he says he doesn't believe other people don't exist.

I really don't think you've provided any "mathematical definition of opposite". — Metaphysician Undercover

I have, twice. But here it is again with the relevant parts bolded:

In mathematics, the additive inverse of a number a is the number that, when added to a, yields zero. This number is also known as the opposite (number),[1] sign change,[2] and negation.[3] For a real number, it reverses its sign: the additive inverse (opposite number) of a positive number is negative, and the additive inverse of a negative number is positive. Zero is the additive inverse of itself. — Additive inverse - Wikipedia

Here's a brief demonstration to help you understand what I am saying. Assume the smallest possible positive number is directly opposed, or inverse, to the largest possible negative number. In other words, we get as close to zero as possible on both sides, and maintain a balance of opposition between the two sides.

Now, let's assume that the quantity represented on each side is so near to nothing (zero) that we might be inclined to round it off. If we do such a thing, then the two quantities on each side become equal to each other, and the same as each other, as zero, instead of opposed to or inverse of one another.

Clearly, two inversely opposed and balancing quantities is not the same thing as one quantity, because that would mean that the positive number closest to zero is exactly the same as the negative number closest to zero, rather than having the two opposed to each other. — Metaphysician Undercover

Yes, I understand. On your definition, the mathematical expression "-(-0)" would be invalid. Is that your intention?

Why isn't there a -0?



That question can be rephrased: why does -0 = 0?

The usual mathematical approach to such a question is to try negating it and seeing what happens.

You should try that. What happens if you have a -0 unequal to 0?

Actually he says he doesn't believe other people don't exist. — Darkneos

So other people exist as per whoever "he" is! :up:

Good is the opposite of bad.

Hot is the opposite of cold.

Yes is the opposite of no.

Same is the opposite of opposite?

I have, twice. But here it is again with the relevant parts bolded:

In mathematics, the additive inverse of a number a is the number that, when added to a, yields zero. This number is also known as the opposite (number),[1] sign change,[2] and negation.[3] For a real number, it reverses its sign: the additive inverse (opposite number) of a positive number is negative, and the additive inverse of a negative number is positive. Zero is the additive inverse of itself.
— Additive inverse - Wikipedia — Andrew M

That's not a definition of opposite, just a use of "opposite" which clearly demonstrates what I said. Your definition of "inverse", as "additive inverse" renders the meaning of "opposite" as inconsistent with common usage. You've demonstrated that by using this definition of inverse, zero is opposite to itself. But a thing being opposite to itself is contrary to common usage of "opposite".

You should try that. What happens if you have a -0 unequal to 0? — Srap Tasmaner

A better thing to try is to consider what happens if a thing is allowed to be opposite to itself. Opposites are commonly the two defining extremes of a measurement scale, hot and cold, big and small, etc.. If we stipulate that the two extremes are the very same thing (like zero relative to the scale), then we have no way to distinguish whether some thing which we're trying to measure, but is off the end of our scale, is off the top of the scale, or off the bottom of the scale, because we have set the conditions whereby the two are the very same (zero relative to the scale).

Opposites are commonly — Metaphysician Undercover

And maybe we do it differently for numbers. What's the opposite of 0? If you take it as "none" then its opposite is "some" which is not a number. What's the opposite of one? In many everyday uses, that's "many" or "several", that is, more than one. What's the opposite of 7? Of 94? What?! I mean, you can always just take 'opposite' as 'complement' within the domain, so the opposite of zero is non-zero, the opposite of 94 is {x in Xs | x =/= 94}, given some domain of Xs.

In math we also have inverses, additive and multiplicative. They're opposite-ish, the way equivalence is equal-ish.

No just that other people exist, I talked with him.

Word games full of sound and fury . . . :roll:

I dunno, I don't really feel that way. I find pre-theoretical intuitions interesting and important. No math without 'em.

I read just the other day that a common counting system (among non-literate peoples) is 1, 2, 3, Many. Don't know if it's true, but if so we've come a long way.

Does quantum physics say nothing is real?

When I get into the philosophy about it I get stuff like "well that depends what you mean by reality", after that I pretty much tune it out. — Darkneos

Late to the party here. I haven't read beyond the first page of posts. But I don't see where the key word has been defined in terms of quantum physics. Hence, the thread has migrated off-topic to loosely relevant notions of "opposition". Anyway FWIW, I'll add my two cents worth on the fraught topic of Reality, which underlies many of the heated disputes on the forum. We seem to split between a narrow physical definition, and a broader metaphysical meaning of "Real".

The early quantum scientists argued among themselves about the same existential question. In his 1958 book, Physics and Philosophy, Werner Heisenberg discussed Descartes' division of the world into "res extensa" (matter) and "res cogitans" (mind). Werner concluded that "the position to which the Cartesian partition has led with respect to the "res extensa" was what one may call metaphysical realism. . . . This is to be distinguished from practical realism." That dichotomy forces us to distinguish between two different uses of the word "real". Then he noted, "actually the position of classical physics is that of dogmatic realism".

Today, some philosophers bow to the empirical authority of Classical Physics, and define "Real" in terms of 17th century Materialism. But a few still see a role for Platonic Idealism ; especially since Quantum Physics emerged, and undermined some of the unproven assumptions for the primacy of matter. For example, the ancient philosophy of Atomism has now crumbled under the onslaught of Quantum reduction into a meta-physical world of amorphous fields of statistical Probability, populated by dimensionless points that are labeled as Virtual Particles.

Despite the philosophical concerns of Quantum pioneers, most physicists today tend to treat "virtual" particles as-if they are "real" lumps of matter, instead of immaterial mathematical concepts of warping "excitations" in a local zone of non-local empty-but-plastic space. So, they are doggedly holding on to the outdated classical definition of "Real". Meanwhile a few contemporary philosophers & scientists are redefining "Real" in the metaphysical terms of Quantum queerness. So, what do you mean by "Real" : pragmatic or philosophical? :smile:



How can we know what's Real? :
In a world of idealistic & imaginative humans, how can we know what's real, and what's fantasy? The scientific method was designed for just that purpose. But it originally assumed a clear distinction between Fact and Fiction. Unfortunately, such a precise dichotomy is no longer realistic, since the thoroughly attested Quantum Theory describes the invisible foundations of our observed universe in terms of entities that are literally-unreal abstractions, verifiable only by inference from paradoxical lab results. In my own personal experience, I have never seen a wishy-washy-waving quantum particle or felt the spooky chill of a quantum field brimming with ghostly unborn particles. Hence, I have to trust the professional physicists who assure me that what I see with my natural senses is not the ultimate reality.
http://www.bothandblog.enformationism.info/page11.html
Note__ The pioneers of Quantum Theory were perplexed by their inability to apply Classical notions of physical reality to what they were finding in their sub-atomic experiments. Niels Bohr: "Everything we call real is made of things that cannot be regarded as real. A physicist is just an atom's way of looking at itself." That last line is prescient of John A. Wheeler's assertion that "We are not only observers. We are participators. In some strange sense, this is a participatory universe".

Realism vs Realistic :
A pertinent philosophical distinction is between Objective reality and Subjective ideality. Or in more technical terms : Phenomena (reality as we know it) and Noumena (ideal reality). Of course, we can only guess at the latter, based on models created from our sense impressions. We only sense the tiny part of Cosmos that is within the limited reach of our physical senses. But our rational minds have allowed us to expand the range of our knowledge of reality. So, we are now aware of an unseen realm, not of ghosts & fairies, but of waves of potential and particles of possibility. To a classical physicist such literal non-sense would sound fantastic. But we moderns now accept such fantasies, because our priests of physics can work miracles, by calling upon the powers of the underworld. I’m kidding, of course, but it’s literally true. For example, flash memory works its magic by producing particles that can pass through solid walls (Quantum Tunneling)⁴¹.
http://bothandblog7.enformationism.info/page54.html

In math we also have inverses, additive and multiplicative. They're opposite-ish, the way equivalence is equal-ish. — Srap Tasmaner

This was the point I was making in the first place. Additive inverse is different from multiplicative inverse, because neither represents a true inversion, they're inverse-ish, each in its own specific way.

No just that other people exist, I talked with him. — Darkneos

How does he know other people exist?

In mathematics, the additive inverse of a number a is the number that, when added to a, yields zero. This number is also known as the opposite (number) — Additive inverse - Wikipedia

A curious statement. All the years I've practiced math I can't recall using "opposite" in this way. But I suppose some do.

I dunno, I don't really feel that way. I find pre-theoretical intuitions interesting and important. No math without 'em. — Srap Tasmaner

Indeed. Centuries ago.

What's the opposite of 0? — Srap Tasmaner

The mathematical answer to that question is different from the philosophical one, oui mon ami?

zero is its own opposite
— Andrew M

Sorry Andrew, but "opposites" don't work that way. A thing is the same as itself, it cannot be opposite to itself. "Opposite" requires two. — Metaphysician Undercover

:cool: but ...

Major Edit : "Opposite" is perfectly fine when discussing positives and negatives. One of the meanings of opposite is "across from". Consider the number line with zero as the value between the positives and negatives. +5 is across from -5. Opposite works.

If quantum physics says blah blah blah then, mon ami, we havta know the meaning of the word "opposite". :cool:

Major Edit : "Opposite" is perfectly fine when discussing positives and negatives. One of the meanings of opposite is "across from". Consider the number line with zero as the value between the positives and negatives. +5 is across from -5. Opposite works. — Real Gone Cat

That doesn't resolve the problem, which relates to zero being a number, as having a place on the line. Is zero across from zero?

I suggest that these false inversions, which are inversion-ish, rather than true inversions, are what create the appearance of symmetries in the application of the mathematical principles which describe something which is not a true inversion as an "inversion". Then symmetries are taken by some philosophers, to be something real, existing in the universe, instead of just a product of the mathematics, and misleading descriptive terms. This has opened a whole new field of speculation into an assumed phenomenon known as "symmetry breaking". But the symmetries are just fictional, imaginary, produced from the misuse of descriptive terms, and so that speculative field of symmetry breaking speculates about the activity of things "symmetries" which don't even exist.

Okay, I'll give it a go. But you usually dig your heels in and refuse to hear otherwise when it comes to math. Try to have an open mind.

I could offer an intro to group theory to prove zero is an inverse of itself, but I don't think that's going to sway someone so math-phobic. Let's stick with the idea in my previous post : Can we agree that "opposite" sometimes means "across from"?

To be across from something means to be reflected in a line, point, or plane. Even when facing a friend at a table we can be said to be reflected in an invisible plane between us (actually reflected in a line to preserve left- and right-handedness).

What's of interest is what happens to points lying on the line (or point or plane) of reflection. Under the reflection, such points do not move! Thus a point on the surface of a mirror will reflect onto itself!

When a reflection in zero is performed on a number line, every point maps to it's negated version, but zero maps to itself. In other words, zero is across from (opposite to) itself.

In other words, zero is across from (opposite to) itself. — Real Gone Cat

If that perspective is valuable to you, then great. It wouldn't be valuable in say, electronic engineering, where zero volts or ground is neutral. You really can't have it that zero volts is also positively or negatively charged.

I think that same situation will hold in most of the ways we use "zero.".

If the domain of mathematics has some other use for the word, I wonder what it could be.

You've demonstrated that by using this definition of inverse, zero is opposite to itself. — Metaphysician Undercover

Thank you.

But a thing being opposite to itself is contrary to common usage of "opposite". — Metaphysician Undercover

Since the unary negation of zero (-0) is a perfectly valid operation, I disagree.

Note that your objection can equally be levelled at "add", which is conventionally defined as "join (something) to something else so as to increase the size, number, or amount."

"3 + 0", and "3 + -1" don't increase the initial number, yet that kind of addition is commonplace. It's a good example of how an idea can be generalized.

Dividing by one is a further example, where "divide" is conventionally defined as "separate or be separated into parts".

Additive inverse is different from multiplicative inverse, because neither represents a true inversion, — Metaphysician Undercover

They are different kinds of inversion. What would a "true inversion" be?

What's of interest is what happens to points lying on the line (or point or plane) of reflection. Under the reflection, such points do not move! Thus a point on the surface of a mirror will reflect onto itself! — Real Gone Cat

Great example!